NO HEAT

1998 Ford Taurus • 6 cylinder •

I have a 98 ford taures 3.0 liter. The car has no heat. I flushed the heater core but found something I've never see in the prosess. Can someone please tell me why the heater core has one solid hose then another hose with a rubber tee one side goes where it supposed to but the other isnt conected to it. Even after I flushed the heater core I still have very low heat. Is that rubber tee supposed to be there.